Problem: Simplify the following expression: $r = \dfrac{4}{3p} + \dfrac{1}{7p}$
Answer: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3p$ and $7p$ $\lcm(3p, 7p) = 21p$ $ r = \dfrac{7}{7} \cdot \dfrac{4}{3p} + \dfrac{3}{3} \cdot \dfrac{1}{7p} $ $r = \dfrac{28}{21p} + \dfrac{3}{21p}$ $r = \dfrac{28 +3}{21p}$ $r = \dfrac{31}{21p}$